考虑畸变影响的箱梁横向弯矩计算方法

为研究偏心垂向荷载作用下梯形截面单室箱梁的横向弯矩,对框架分析法计算箱梁横向弯矩的方程进行优化,并在刚性支承法的基础上提出一种更加简单的横向弯矩计算方法;与框架分析法不同,横向弯矩可采用能量变分法求解,建立以箱梁顶板剪力差为未知量的四阶控制微分方程,采用比拟的弹性地基梁解法解出剪力差,得出梯形截面单室箱梁横向弯矩的能量变分法解。对几种箱梁横向弯矩计算方法用两个算例进行验证,结果表明,能量变分法解将箱梁底板上的弯矩误差绝对值由15.41%降到了9.68%;本文方法得出的横向弯矩结果和有限元结果吻合较好,弯矩误差绝对值最大不超过6.01%;本文方法和能量变分法可有效降低箱梁底板上的弯矩误差,计算精度得到提高。     

轴对称薄壁结构自由振动的边界元分析

采用双互易法分析薄壁轴对称结构自由振动的特征频率以及特征模态.首先,采用径向基函数插值域积分里的位移,利用双互易法将域积分转化为子午面边界的积分.然后,将边界物理量、基本解和特解展开为傅里叶级数,沿环向积分后得到的边界积分方程可用于轴对称结构带体积力问题和受非对称载荷的动力学分析,其积分域为轴对称结构子午面边界上的线积分,进一步降低了问题的维度和离散的难度.文章详细探讨了源点处于对称轴的特殊情况,根据基本解和特解的退化形式,针对无体积力和有体积力分别给出了处理奇异矩阵的方案.对于薄壁结构,采用双曲正弦变换处理近奇异积分有效提高积分精度.最后将双互易法和双曲正弦变化应用于薄壁轴对称结构带体积力的静力学和自由振动分析.数值结果表明,文章提出的处理奇异矩阵的方法能够有效处理源点处于对称轴的情况;当圆筒厚高比为$10^{-3}$,边界元计算的特征频率的相对误差为$10^{-3}$,且优于有限元的结果.      

Dynamic behaviour of a bubble near an elastic infinite interface

This paper presents a study to describe the behaviour of a non-equilibrium bubble in a fluid (Fluid 1) that is in contact with another fluid (Fluid 2). Fluid 2 is assumed to incorporate some elastic properties, which are modelled through a pressure term at the fluid–fluid interface. The Laplace equation is assumed to be valid in both fluids and the boundary integral method is employed to simulate the dynamics of the bubble and the fluid–fluid interface. Interesting characteristic phenomena concerning bubble oscillations and the deformation of the fluid–fluid interface are studied for a range of parameters (distance from the fluid–fluid interface, density ratios of the two fluids and elastic properties of Fluid 2). Some of the phenomena observed are jet formation in the bubble, bubble splitting, a ring bubble separating from the main bubble, mushroom-shaped bubbles and the dynamic elevation of the elastic interface. Most of these phenomena are only observed when Fluid 2 possesses some elastic properties (besides the usual formation of a high speed liquid jet). Comparisons with experimental observations confirm the validity of our simulations.     

区段混合能的偏微分方程

结构力学与最优控制模拟关系的共同基础就是分析力学，表明在结构力学与最优控制理论的架构内也应有分析力学的整套理论。传统分析力学总是考虑连续时间、同时的状态、不变维数的体系。并且物性为即时响应的。但结构力学有限元要考虑离散坐标、不同坐标状态、而且变动维数、时滞的体系。根据区段变形能只与其两端位移有关，就可通过数学分析得到Lagrange括号与Poisson括号等内容。区段变形能就是作用量，满足Hamilton-Jacobi方程。但还有区段混合能的表示，本文证明它满足雷同的偏微分方程。它们在离散体系时还有偏差分方程。本文进一步给出了其与Riccati方程的关系。     

受扰细杆的Melnikov分析

研究了计入Peierls-Nabarro (P-N)力和固体黏性效应的一维金属杆在简谐外力扰动下的动力响应，其位移波的运动规律是Sine-Gordon (SG) 型方程. 采用集结坐标 (collective coordinate)将方程的解设为未扰系统呼吸子解的形式，研究扰动作用下，组成呼吸子的扭结-反扭结波的中心的分离. 通过用集结坐标表示系统的哈密顿量，从而将SG型方程转化为常微分方程组. 分析了未扰系统的异宿轨道，并将之用于Melnikov方法对系统进行分析，给出横截异宿点出现的必要条件，从而预测混沌运动的发生.     

多体系统动力学设计灵敏度分析直接微分法

针对受完整约束的多体系统动力学微分／代数方程数学模型动态最优化设计问题，建立了通用的目标函数和约束方程，并以此为基础，用直接微分方法系统地推导出了计算设计灵敏度的通用公式，最后通过平面机械臂模型对理论结果和相应算法进行了验证．     

横观各向同性压电材料中裂纹问题的边界元法

采用Somigiliana公式给出了三维横观各向同性压电材料中的非渗漏裂纹问题的一般解和超奇异积分方程，其中未知函数为裂纹面上的位移间断和电势间断．在此基础上，使用有限部积分和边界元结合的方法，建立了超奇异积分方程的数值求解方法，并给出了一些典型数值算例的应力强度因子和电位移强度因子的数值结果，结果令人满意．     

透平机械离心压缩机和离心泵叶轮动力分析的三维旋转循环对称CN群算法

以离心压缩机叶轮为例,建立三维有限元模型,采用循环对称CN群算法计算了它的动力特性,详细讨论离心力作用下叶轮的应力状态,分析与轴连接的不同方式对叶轮应力的影响。应用循环对称算法能大大减少建模与计算的工作量,有很好的实用价值。计算结果表明,离心压缩机叶轮在旋转中,叶轮外缘应力比较高,轮盖上的应力较轮盘上的应力大,叶片根部容易产生应力集中,应采用适当的园角避免应力集中,过盈配合的叶轮内孔处应力比较大,需要确定合理的过盈量,既要保证叶轮不松动也要保证叶轮内孔处的强度条件。     

A NOVEL SEMI-ANALYTICAL METHOD FOR SOLVING ACOUSTIC RADIATION FROM LONGITUDINALLY STIFFENED INFINITE NON-CIRCULAR CYLINDRICAL SHELLS IN WATER

Based on the extended homogeneous capacity high precision integration method and the spectrum method of virtual boundary with a complex radius vector, a novel semi-analytical method, which has satisfactory computation effectiveness and precision, is presented for solving the acoustic radiation from a submerged infinite non-circular cylindrical shell stiffened by longitudinal ribs by means of the Fourier integral transformation and stationary phase method. In this work,besides the normal interacting force, which is commonly adopted by some researchers, the other interacting forces and moments between the longitudinal ribs and the non-circular cylindrical shell are considered at the same time. The effects of the number and the size of the cross-section of longitudinal ribs on the characteristics of acoustic radiation are investigated. Numerical results show that the method proposed is more efficient than the existing mixed FE-BE method.     

Natural Vibrations of a Cylindrical Shell with Circular Ribs Attached by Means of Discrete Elastic Elements

The vibrations of a cylindrical shell reinforced with circular ribs attached to it by means of discrete elastic elements are studied. The problem is solved by the finite-element method. The shell and ribs are modeled by a plane four-node finite element, which is a combination of a four-node plane stress element and a four-node flexural element. The effect of the stiffness of the elastic elements on the natural frequencies and modes is examined __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 108–113, October 2005.